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This paper discusses a cooperative strategy for capturing a target using multiple pursuers in a planar scenario. Given an initial position distribution of pursuers, the Voronoi Diagram is employed to characterize the target's proximity region. The key idea is to dynamically shape that region using a policy that directs its vertices towards its instantaneous centroid. Analysis of the resulting dynamics deduces the velocity control inputs for the pursuers. As the main result, target's proximity region is shown to shrink exponentially irrespective of its speed and evasion policy. Simulation results demonstrate the characteristics of the proposed method.

One mechanistic interpretation of baroclinic instability is that of mutual constructive interference of Rossby edge-waves. While the two edge-waves and their relative phase-shifts are invoked as part of the mechanistic interpretation, the phase-tilts of the related normal modes are often presented instead. Here we highlight the differences between edge-wave phase-shifts and normal-mode phase-tilts, in the context of an Eady problem modified by the presence of a sloping boundary. We argue and present evidence that the normal-mode phase-tilt is potentially a misleading quantity to use, and edge-wave phase-shifts should be the ones that are mechanistically relevant. We also provide a clarification for the mechanistic rationalization for baroclinic instability in the presence of slopes (such as suppression of growth rates) that is valid over all parameter space, in contrast to previous attempts. We further present evidence that there is a strong correlation between quantities diagnosed from the GEOMETRIC framework with the edge-wave phase-shifts, but not the normal-mode phase-tilts. The result is noteworthy in that the geometric framework makes no explicit reference to the edge-wave structures in its construction, but the correlation suggests that in problems where edge-wave structures are not so well-defined or readily available, the GEOMETRIC framework should still capture mechanistic and dynamical information. Some implications for parameterization of baroclinic instability and relevant eddy-mean feedbacks are discussed. For completeness, we also provide an explicit demonstration that the linear instability problem of the present modified Eady problem is parity-time symmetric, and speculate on some suggestive links between parity-time symmetry, shear instability, and the edge-wave interaction mechanism., Comment: 9 figures; discrepancy of arXiv abstract and file abstract, because number of characters exceeded in arXiv version

This article considers the problem of conflict-free distribution of agents on a circular periphery encompassing all agents. The two key elements of the proposed policy include the construction of a set of convex layers (nested convex polygons) using the initial positions of the agents, and a novel search space region for each of the agents. The search space for an agent on a convex layer is defined as the region enclosed between the lines passing through the agent's position and normal to its supporting edges. Guaranteeing collision-free paths, a goal assignment policy designates a unique goal position within the search space of an agent at the initial time itself, requiring no further computation thereafter. In contrast to the existing literature, this work presents a one-shot, collision-free solution to the circular distribution problem by utilizing only the initial positions of the agents. Illustrative examples demonstrate the effectiveness of the proposed policy.

Control of a dynamical system without the knowledge of dynamics is an important and challenging task. Modern machine learning approaches, such as deep neural networks (DNNs), allow for the estimation of a dynamics model from control inputs and corresponding state observation outputs. Such data-driven models are often utilized for the derivation of model-based controllers. However, in general, there are no guarantees that a model represented by DNNs will be controllable according to the formal control-theoretical meaning of controllability, which is crucial for the design of effective controllers. This often precludes the use of DNN-estimated models in applications, where formal controllability guarantees are required. In this proof-of-the-concept work, we propose a control-theoretical method that explicitly enhances models estimated from data with controllability. That is achieved by augmenting the model estimation objective with a controllability constraint, which penalizes models with a low degree of controllability. As a result, the models estimated with the proposed controllability constraint allow for the derivation of more efficient controllers, they are interpretable by the control-theoretical quantities and have a lower long-term prediction error. The proposed method provides new insights on the connection between the DNN-based estimation of unknown dynamics and the control-theoretical guarantees of the solution properties. We demonstrate the superiority of the proposed method in two standard classical control systems with state observation given by low resolution high-dimensional images.